1. Field of the Invention
The present invention generally relates to a digital filter that passes a required frequency. In particular, the present invention relates to an adaptive digital filer provided with a coefficient renewal unit for minimizing the variation between input data and output data.
2. Description of the Related Art
FIG. 17 shows a conventional adaptive digital filter (generally indicated by reference numeral 100) which includes an IIR (infinite impulse response) digital filter 101 and a coefficient controller 102 for controlling the coefficient a to determine the central frequency of the pass band of the filter. Whenever digital data (sampling data) x[n] is inputted to the filter 101, calculation is performed to determine a coefficient a[n+1] which minimizes the difference e[n]=x[n]−y[n], where y[n] is an output from the filter. The calculation result is used for the filter 101 when the next digital data x[n+1] is inputted to the filter. In this manner, it is possible to allow only a desired frequency f0 to pass through.
The renewal of the coefficient a[n+1] of the conventional filter 100 is performed in accordance with Formula (1) below:
                              a          ⁡                      [                          n              +              1                        ]                          =                              a            ⁡                          [              n              ]                                +                                    β              ·                              e                ⁡                                  [                  n                  ]                                            ·                              u                ⁡                                  [                                      n                    -                    1                                    ]                                                                                                      u                  ⁡                                      [                    n                    ]                                                  2                            +                                                u                  ⁡                                      [                                          n                      -                      1                                        ]                                                  2                                                                        (        1        )            
According to S. Haykin's ‘Adaptive Filter Theory, 3rd ed. (published in 1996), when the factor β in Formula (1) satisfies 0<β<2, the renewal value a[n+1] of the coefficient a converges to a definite value.
FIG. 18 shows a circuit for calculating the coefficient a based on Formula (1). This coefficient calculating circuit includes a divisor calculator 103 (for determining the value of u[n]2+u[n−1]2), a dividend calculator 104 (for determining the value of e[n]·u[n−1]), a division circuit 105 (for determining the quotient (e[n]·u[n−1])/(u[n]2+u[n−1]2)), a multiplier 106 (for calculating the product of the factor β and the quotient calculated by the division circuit 105), and an adder 107 (for adding the previously calculated a[n] and the calculation result from the multiplier 106).
Such a technique as described above is disclosed in JP-A-H06-188683 and JP-B2-3092647, for example.
The coefficient controller 102 of the conventional filter has been found disadvantageous in that the coefficient a is calculated by Formula (1), which makes the arrangements of the division circuit 105 complex and large. Accordingly, the calculation time tends to be unduly long.
More specifically, when the coefficient renewal calculation is performed in accordance with Formula (1), it is possible to calculate an accurate renewal value a[n+1]. However, the expected function of the coefficient controller 102 is to calculate a definite coefficient with which only a single frequency f0 is allowed to pass the filter. Therefore, as long as the desired frequency filtering is attained, the coefficient renewal is not necessarily performed by Formula (1).
If Formula (1) could be replaced by a different formula which permits simple and high-speed digital processing, it would be possible to produce an adaptive digital filter with a simple and high-speed coefficient renewal circuit.